Page 275 - Materials Chemistry, Second Edition

13.2 Decision-making under multi-type data condition 273
Definition 13.7 Addition between intuitionistic fuzzy numbers (Xu and Yager, 2006).
Let γ ¼(μ γ ,υ γ ,π γ ) and β¼(μ β ,υ β ,π β ) be two intuitionistic fuzzy numbers; the addition operation
between these two intuitionistic fuzzy numbers can be determined by Eq. (13.12).
(13.12)
A B
B
A
A
B
A B
B
A
ð
ð
A B ¼ μ , υ A , π A Þ μ , υ B , π B Þ ¼ μ + μ μ μ , υ A υ B ,1 + μ μ μ μ υ A υ B Þ
ð
0 1
n n n n
n n Y Y Y Y
1 μ 1 μ
@ , , A (13.13)
A j ¼ μ , υ A j , π A j ¼ 1 υ A j υ A j
A j A j A j
j¼1 j¼1
j¼1 j¼1 j¼1 j¼1
Definition 13.8 Scale multiplication (Xu and Yager, 2006).
Let A¼(μ A ,υ A ,π A ) be an intuitionistic fuzzy set and λ be a real number, then,

λ λ λ λ
A
ð
ð
λA ¼ 1 1 μ Þ , υ A Þ ,1 μð A Þ υ A Þ (13.14)
ð
The criteria determined by LCA, LCC, and SLCA can be divided into two types: the
so-called soft criteria and hard criteria. The data of the alternative industrial or energy sys-
tems with respect to the “hard” criteria can be determined through field survey, simulation,
estimation, and calculation, based on the LCA database or software. However, the data with
respect to the “soft” criteria usually cannot be quantified or described in a quantitative way.
Moreover, the alternative industrial or energy systems usually involve different stakeholders
and different stakeholders have different willingness, preferences, and interests. Therefore, it
is usually difficult to determine the data of the alternative industrial or energy systems with
respect to the “soft” criteria. Therefore, a novel way for determining the data with respect to
the “soft” criteria was developed in this study, and it consists of four steps:
Step 1: Determining all the groups of stakeholders. A representative stakeholder will be
selected for each group to collect the preferences, opinions and interests of each group.
A focus group meeting can be held to determine the relative performances of the alternative
industrial or energy systems with respect to the “soft” criteria based on the opinions of each
group of stakeholders. The representative stakeholder in each group will work as the coor-
dinator, and a consensus will be achieved in each group.
Step 2: Rate the alternative industrial or energy systems with respect to each “soft” crite-
rion (Zhou et al., 2005). The stakeholders are asked to use the eleven linguistic variables to
describe the relative performances of the alternatives with respect to the “soft” criteria,
and they are absolutely good (AG), very good (VG), good (G), pretty good (PG), moderately
good (MG), medium (M), moderately bad (MB), pretty bad (PB), bad (B), very bad (VB),
and absolutely bad (AB). AG, VG, G, PG, MG, M, MB, PB, B, VB, and AB correspond
to ten intuitionistic fuzzy numbers, which are (1,0,0), (0.90,0.05,0.05), (0.80,0.10,0.10),
(0.70,0.15,0.15), (0.60, 0.20,0.20), (0.50,0.50,0), (0.40,0.40,0.20), (0.30,0.55,0.15), (0.20,0.70,0.10),
(0,.10,0.85,0.05), and (0,1.00,0), respectively (Zhou et al., 2005).
Step 3: Determining the data of the alternatives with respect to each “soft” criterion.
Assuming that there are a total of K groups of stakeholders, and the kth group of stakeholders
k
k
k
k
use the intuitionistic fuzzy numbers A ij ¼(μ ij ,υ ij ,π ij ) to describe the relative performances of
the ith alternative with respect to the jth criterion, which is a “soft” criterion. According to